Core Concepts
The core message of this article is to derive less conservative sufficient conditions for the robust feedback stability of linear time-invariant systems involving sectored-disk uncertainty, which encompasses simultaneous gain and phase constraints on the uncertain dynamics.
Abstract
The article investigates the robust feedback stability problem for multiple-input-multiple-output linear time-invariant systems with sectored-disk uncertainty, which refers to dynamic uncertainty subject to simultaneous gain and phase constraints.
Key highlights:
- The authors leverage the notion of the Davis-Wielandt (DW) shell, a higher-dimensional generalization of the numerical range, to characterize the shape of the DW shell union of sectored-disk matrices.
- Based on the DW shell analysis, the authors derive a fundamental static matrix problem that serves as a key component in addressing the feedback stability.
- A sufficient condition and a necessary condition for the matrix sectored-disk problem are established, providing a less conservative approach compared to using the small gain theorem and the small phase theorem alone.
- Several linear matrix inequality-based conditions are developed for efficient computation and verification of feedback robust stability against sectored-disk uncertainty.
The article provides a comprehensive analysis of the robust stability problem involving simultaneous gain and phase constraints, offering insights into the interplay between norm and phase information in feedback systems.